Real-time single-pixel video imaging with Fourier domain regularization

Abstract

We present a closed-form image reconstruction method for single pixel imaging based on the generalized inverse of the measurement matrix. Its numerical cost scales linearly with the number of measured samples. Regularization is obtained by minimizing the norms of the convolution between the reconstructed image and a set of spatial filters, and the final reconstruction formula can be expressed in terms of matrix pseudoinverse. At high compression this approach is an interesting alternative to the methods of compressive sensing based on l1-norm optimization, which are too slow for real-time applications. For instance, we demonstrate experimental single-pixel detection with real-time reconstruction obtained in parallel with the measurement at the frame rate of $11$ Hz for highly compressive measurements with the resolution of $256\times 256$. For this purpose, we preselect the sampling functions to match the average spectrum obtained with an image database. The sampling functions are selected from the Walsh-Hadamard basis, from the discrete cosine basis, or from a subset of Morlet wavelets convolved with white noise. We show that by incorporating the quadratic criterion into the closed-form reconstruction formula, we are able to use binary rather than continuous sampling reaching similar reconstruction quality as is obtained by minimizing the total variation. This makes it possible to use cosine or Morlet-based sampling with digital micromirror devices without advanced binarization methods.

References in corpus (9)

• Sparsity and Incoherence in Compressive Sampling
• NESTA: A Fast and Accurate First-order Method for Sparse Recovery
• Single-pixel 3D imaging with time-based depth resolution
• Experimental comparison of single-pixel imaging algorithms
• Multispectral imaging using a single bucket detector
• Single-pixel imaging with Morlet wavelet correlated random patterns
• Two-pixel polarimetric camera by compressive sensing
• Compressive phase-only filtering at extreme compression rates
• Computational Ghost Imaging

Cited by in corpus (7)

• Image watermarking and fusion based on Fourier single-pixel imaging with weighed light source
• Single pixel imaging at high pixel resolutions
• Differential real-time single-pixel imaging with Fourier domain regularization -- applications to VIS-IR imaging and polarization imaging
• Single-pixel imaging with sampling distributed over simplex vertices
• Instant Ghost Imaging: Algorithm and On-chip Implementation
• A detail-enhanced sampling strategy in Hadamard single-pixel imaging
• Single-pixel imaging via data-driven and deep image prior dual networks